Question

Find

-A continuous r.v. X follows uniform distribution , that is ? ~ ???????(?=0,?=1), Find the following probability
(a) P(0 < X < 0.3)
(b) P(0.5 < X < 1)
(c) Find the mean and variance of X

- A continuous r.v. X follows the pdf: ?(?)= 2?3, 1≤?≤2.
(a) Find the cdf of X for 1≤?≤2.
(b) Find the mean and variance of X.
(c) Find P(X = 1.22)

-Suppose that in a particular traffic environment, the distribution of time headway has the following form.
?(?)={??−2? ?≥00 ?<0
Determine the value of k for which f(x) is a valid pdf.

- The cdf of a r.v. X is given by:
?(?)={1−?−0.5? ?≥00 ?<0
Find the pdf of X

- An engineer designs a new battery to be used in a handheld calculator. The lifetime of the battery is exponentially distributed and has and expected lifetime of μ = 4000 hours.
(a). Given that the expected lifetime is μ = 4000 hours, what is the value of λ?
(b). What is the probability that the lifetime of the battery is less than 5000 hours? Clearly specify the probability statement!!
(c). What is the probability that the lifetime of the battery is exactly 2000 hours?

Answer 1

Variables in all other questions are not visible .

So i m unable to do other questions.